2:15pm-3:55pm Monday and Wednesday in room 276 MSB.
Also note:
Section Start Date 01/16/18; Section End Date 05/06/18; Last Day to Add 01/21/18; Last Day to Drop 01/28/18; Last Day to Withdraw 03/25/18;
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Instructor: Books: Office hours: Office: Office tel.: E-mail: WWW of the course : |
Artem Zvavitch “Complex Analysis” (Princeton Lectures in Analysis, No. 2) by E. M. Stein, R. Shakarchi. I may also use “Complex Analysis” by Lars V. Ahlfors. 12:30-2:00 MW, but the best is to e-mail me and to make an appointment. 364 (330)-672-33-16 zvavitch@math.kent.edu http://www.math.kent.edu/~zvavitch/CV_2018.html |
Please, note the calendar below is just a plan. Homework and Exams dates may be adjusted during the semester!
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Date
|
Lecture Topic
|
Special Remarks
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Wednesday (01/17/18) |
A short reminder about Complex Numbers | First Homework. |
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Monday (01/22/18) |
A bit more basic properties. Continuos functions. Holomorphic functions. | |
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Wednesday (01/24/18) |
Holomorphic functions. Welcome to power series | Second Homework. First Homework Due. |
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Monday (01/29/18) |
A bit more about power series. First look at complex integration | |
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Wednesday (01/31/18) (NOTE we will start at 2:05) |
Complex Integration and Cauchy's theorem | Third Homework. Second Homework Due. |
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Monday (02/05/18) (NOTE we will start at 2:05) |
Cauchy's theorem. | |
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Wednesday (02/07/18) (NOTE we will start at 2:05) |
Applications of Cauchy's theorem and Cauchy Integral. Applications: Liouville's theorem. Fundamental theorem of algebra. | Fourth Homework. Third Homework Due. |
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Monday (02/12/18) (NOTE we will start at 2:05) |
More Applications: analytic continuation. Morera's theorem. Sequences of holomorphic functions. | |
|
Wednesday (02/14/18) |
Schwarz reflection principle. Runge's approximation theorem. | Fifth Homework. Forth Homework Due. |
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Monday (02/19/18) |
Runge's approximation theorem. Welcome to zeros, poles. | |
|
Wednesday (02/21/18) |
Zeros, poles and Meromorphic Functions. Examles of applications to "real" integral and Riemann's theorem on removable singularities. | Sixth Homework. Fifth Homework Due. |
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Monday (02/26/18) |
Meromorphic functions and more discussion of singularities. Casorati-Weierstrass theorem and more. | |
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Wednesday (02/28/18) |
Argument Principle/ Rouche's Theorem /Maximum modulus principle | Sevens Homework. Sixth Homework Due. |
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Monday (03/05/18) |
Homotopies and Simply connected Domain and another look at integrals. | |
|
Wednesday (03/07/18) |
The complex logarithm and the mean-value property. | Eigts Homework. Sevens Homework Due. |
|
Monday (03/12/18) |
Entire Functions and Jensen's formula. Conting the roots. Functions of finite order | |
|
Wednesday (03/14/18) |
Functions of finite order. Welcome to Infinite product. | Nine's Homework. Eights Homework Due. |
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Monday (03/19/18) |
Infinite Products. Weierstrass factorization theorem. | |
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Wednesday (03/21/18) |
Hadamard factorization theorem. | Ten's Homework. Nines Homework Due. |
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Monday (03/26/18) |
NO CLASS, SPRING BRAKE | |
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Wednesday (03/28/18) |
NO CLASS, SPRING BRAKE | |
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Monday (04/02/18) |
Welcome to conformal mappings. | |
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Wednesday (04/04/18) |
Conformal Mappings, Schwartz lemma and automorphism of the disc. | Elleven's Homework. Ten's Homework Due. |
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Monday (04/9/19) |
Automorphisms of the disc and upper half-plane. | |
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Wednesday (04/11/18) |
Riemann mapping Theorem. | Twelve's Homework. Elleven's Homework Due. |
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Monday (04/16/18) |
Riemann mapping Theorem. Conformal mappinngs onto polygons. | |
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Wednesday (04/18/18) |
Conformal mappinngs onto polygons: Schwartz-Christoffel integral. | Homework Thirteen. Twelve's Homework Due. |
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Monday (04/23/18) |
Conformal mappinngs onto polygons:Boundary behaviour | |
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Wednesday (04/25/18) |
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Monday (04/30/18) |
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Wednesday (05/02/18) |
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May 13 |
FOR FINAL HOME WORK Please do problems 1,2,3,4,5 from 2015 Qual. Exam and problems 6,7,8,9,10 from 2017 Qual. Exam . | |